1. The problem is to determine who performed better based on z-scores. 2. To find who performed better, recall that a higher z-score means better performance relative to the mean. 3. a) Ping's z-score is 1.60, Pong's is 1.75. Since 1.75 > 1.60, Pong performed better. 4. b) Sol's z-score is -1.5, Buddy's is -2.0. Since -1.5 > -2.0, Sol performed better. --- 5. Problem 2: Find z-scores for grades given mean $\mu=81$ and standard deviation $\sigma=5$. 6. Use the formula for z-score: $$z=\frac{x-\mu}{\sigma}$$ 7. a) Leand: $z=\frac{70-81}{5}=\frac{-11}{5}=-2.2$ 8. b) Louis: $z=\frac{91-81}{5}=\frac{10}{5}=2$ 9. c) Chris: $z=\frac{60-81}{5}=\frac{-21}{5}=-4.2$ 10. d) Leo: $z=\frac{85-81}{5}=\frac{4}{5}=0.8$ 11. e) Evelyn: $z=\frac{96-81}{5}=\frac{15}{5}=3$ --- 12. Problem 3: Find grades $x$ given z-scores using formula: $$x=\mu + z\sigma$$ 13. a) Pepe, $z=1$: $x=81 + 1 \times 5=86$ 14. b) Ding, $z=-2$: $x=81 + (-2) \times 5=81 - 10=71$ 15. c) Lorna, $z=-2.5$: $x=81 + (-2.5) \times 5=81 - 12.5=68.5$ 16. d) Sam, $z=1.25$: $x=81 + 1.25 \times 5=81 + 6.25=87.25$ 17. e) Lito, $z=2.35$: $x=81 + 2.35 \times 5=81 + 11.75=92.75$ --- 18. Problem 4: Compare Michael's performance in two seasons based on z-scores for scoring 26 points. 19. Season 30: Mean $\mu=24$, $\sigma=6$. Compute z-score: $$z=\frac{26 - 24}{6}=\frac{2}{6}=0.33$$ 20. Season 31: Mean $\mu=19$, $\sigma=5$. Compute z-score: $$z=\frac{26 - 19}{5}=\frac{7}{5}=1.4$$ 21. Since season 31's z-score $1.4 > 0.33$, Michael performed better in season 31. --- 22. Problem 5: Find Robin's earnings given z-score $z=-0.91$, mean $\mu=540$, standard deviation $\sigma=11$. 23. Use formula: $$x=\mu + z\sigma=540 + (-0.91) \times 11=540 - 10.01=529.99$$ 24. Robin earned approximately 530 on that day. Final answers: 1.a) Pong performed better. 1.b) Sol performed better. 2.a) $z=-2.2$ 2.b) $z=2$ 2.c) $z=-4.2$ 2.d) $z=0.8$ 2.e) $z=3$ 3.a) $86$ 3.b) $71$ 3.c) $68.5$ 3.d) $87.25$ 3.e) $92.75$ 4. Michael performed better in season 31. 5. Robin earned about 530.